I think I do not understand this challenge. From the text:

A universal cycle is a cycle where all sets of 3 different values appear exactly once in consecutive neighbors.

It follows that I should "make" each possible set of three values exactly once. Checking the existing sets (before I fill the gaps), I see that for example the sets:

[6,7,9]

[7,8,9]

are not present. The only way to make one of the above sets is to write it in the three consecutive blanks. Once I select one of them, there is no way to "make" the other. What am I missing?